| Title: | Quadratic Approximations to Pi, or What if Archimedes Had Had Mathematica? |
| Speaker: | Mark Bollman Associate Professor Department of Mathematics and Computer Science Albion College |
| Abstract: | Archimedes (c. 287 BCE--c. 212 BCE) used polygons inscribed within and circumscribed about a circle to approximate pi. In this talk, we will extend his work by approximating the areas of circular sectors. This is done by adjoining parabolic segments to triangular subregions of his inscribed regular polygons. While much of the mathematics would have been familiar to Archimedes, the calculations involved quickly outstrip the computational power of ancient Greece, and so Mathematica is used to facilitate calculations. The method allows us to derive recurrence relations that can be used to approximate pi more accurately. |
| Location: | Palenske 227 |
| Date: | 2/17/2011 |
| Time: | 3:10 PM |
@abstract{MCS:Colloquium:MarkBollman:2011:2:17,
author = "{Mark Bollman}",
title = "{Quadratic Approximations to Pi, or What if Archimedes Had Had Mathematica?}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month = "{17 February}",
year = "{2011}"
}